Most 1.6 Earth-Radius Planets are not Rocky Introduction Sub-Neptune, super-Earth-size exoplanets are a new planet class. They account for 0% of the solar.

Most 1.6 Earth-Radius Planets are not Rocky

IntroductionSub-Neptune, super-Earth-size exoplanets are a new planet class. They account for 0% of the solar systems planets, and 80% of the planet candidates discovered by Kepler. For most planets, Kepler measures just the planet radius and orbital period. When Kepler finds a planet with radius Rp, how likely is that planet to be rocky (with its transit radius defined by a rocky surface) versus a mini-Neptune with a thick envelope of H/He and/or astrophysical ices?

Objective: To quantitatively constrain the fraction of planets that are sufficiently dense to be rocky, as a function of planet size, using the sub-sample of Kepler transiting planets with Keck-HIRES radial velocity mass constraints.

Which Planets are Rocky?

Leslie Rogers, Hubble Fellow, [email protected]

Planet Sample

Figure 1: Planet Mass-Radius Diagram. Our sample comprises the transiting Kepler planets with Keck HIRES RV follow-up, highlighted in red (Marcy et al. 2014). Other confirmed transiting sub-Neptune-size planets are indicated with black points. The colored curves are theoretical mass-radius relations for constant planet compositions from Seager et al. (2007) .

Pure silicate places an extreme lower limit on the mass of a volatile-less rocky planet of specified radius. Less dense planets must have some volatiles (in the form of water or H/He), while more dense planets could potentially be rocky, comprised of iron and silicates alone. Mass-radius pairs that are more density than pure iron are unphysical. .

Mp

Rp y, data)

Figure 4: Joint posterior pdf for Rmid and DR. The two-parameter linear rocky/non-rocky transition model allows for a range of radii (of width DR centered on Rmid) at which high-mass rocky planets and low-mass non-rocky planets co-exist. The planet mass-radius data are consistent with an abrupt transition (DR=0).

P(e)

Bayesian EvidenceFavors Step Function

ModelE = Ep(data|a)p(a)da

E1 = 4.9 E2 = 5.0 E3

3. Linear Transition

Results

1. Step Function Transition

Figure 5: The posterior pdf of frocky conditioned on planet radius, Rp. For specified Rp, a vertical slice through this figure corresponds to p (frocky|Rp, data), and quantifies how the Kepler+Keck RV planets constrain the fraction of Rp-size planets that are dense enough to be rocky. Red values of frocky are favored by the data, while blue values are disfavored.

Figure 3: Posterior pdf of Rthresh0 and dRthresh/dlogF. In this two-parameter model, the rocky/non-rocky threshold depends on the amount of irradiation the planet is receiving from its star, Fp. The planet mass-radius data are consistent with no incident flux dependence (dRthresh/dlogF=0).

Rmid = 1.29 +0.23

-0.54 R

< 1.62 R at 95% conf.(marginalized over DR)

Rp

frocky

Rmid

DR

Median 1.48 R

95th Percentile,1.59 R

p (R

thre

sh |d

ata)

Rthresh (R)

Figure 2: Posterior pdf of Rthresh The black curve gives the posterior probability of the rocky/non-rocky threshold in the one-parameter step-function model, wherein all planet larger than Rthresh have volatiles, while all planets smaller than Rthresh are dense enough to be rocky.

dRthresh/dlogF = 0.11 +0.35 -0.12 R

(marginalized over Rthresh0)

Rp

frocky

Rthresh 0

F0 F

Rp

frocky

Rthresh

MethodA hierarchical bayesian analysis approach is adopted.

A flat prior on planet mass and radius is typically assumed when fitting RV and transit data. In the hierarchical analysis, the priors on planet Mp and Rp are opened to modeling. The underlying population of planets has some intrinsic distribution of properties; some Mp-Rp pairs are more likely than others.

A model is chosen for,frocky(Rp, Fp, a) = fraction of planets dense enough to be rocky a = model parameters (constrained

using a resampling approach similar to Hogg et al. 2010)

Mp

Rp

Rp

Mp

ReferencesHogg, D. W., Myers, A. D., & Bovy, J. 2010, ApJ, 725, 2166Marcy, G., Isaacson, H., Howard, A. W., et al. 2014, ApJS, 210, 20Rogers, L. A. (2014) ApJ, submittedSeager, S., Kuchner, M., Hier-Majumder, C. A., & Militzer, B. 2007, ApJ, 669, 1279

I would like to thank Howard Isaacson and Geoff Marcy for sharing samples from their MCMC fits to the Keck-HIRES RV and Kepler photometry data. I also acknowledge support from support provided by NASA through Hubble Fellowship grant #HF-51313.01

Conclusions• Most planets larger than 1.6 R are not rocky, at 95% statistical confidence.• This gives insights into the compositions of the 1000s of Kepler planet

candidates without measured masses, and motivates an operational definition of “Earth-like” for calculating the occurrence rate of Earth-analogs, h.

• frocky sets an upper bound on the fraction of close-in planets formed after protoplanetary disk dispersal.

• More planet Mp-Rp points with smaller error bars are needed to resolve the structure of the transition between rocky and non-rocky planets.

MgSiO3

H2O

Fe

2. Flux-Dependent Step Function Transition